Problem: Simplify to lowest terms. $\dfrac{54}{72}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 54 and 72? $54 = 2\cdot3\cdot3\cdot3$ $72 = 2\cdot2\cdot2\cdot3\cdot3$ $\mbox{GCD}(54, 72) = 2\cdot3\cdot3 = 18$ $\dfrac{54}{72} = \dfrac{3 \cdot 18}{ 4\cdot 18}$ $\hphantom{\dfrac{54}{72}} = \dfrac{3}{4} \cdot \dfrac{18}{18}$ $\hphantom{\dfrac{54}{72}} = \dfrac{3}{4} \cdot 1$ $\hphantom{\dfrac{54}{72}} = \dfrac{3}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{54}{72}= \dfrac{2\cdot27}{2\cdot36}= \dfrac{2\cdot 3\cdot9}{2\cdot 3\cdot12}= \dfrac{2\cdot 3\cdot 3\cdot3}{2\cdot 3\cdot 3\cdot4}= \dfrac{3}{4}$